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People in Group Theory

This page contains web pointers to information about some of the people behind the group theory.

Galilei Galileo  (1564-1642) 

Galilean relativity.  Galileo did not have the mathematical idea of a group but perceived directly the importance of the equivalence of inertial frames. The Galileo group is the inertial relativity group of classical mechanics.

Galileo

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Henrik Abel  (1802-1829) 

Abelian groups.

abelstort

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Evariste Galois  (1811-1832) 

Founded key concepts in group theory in the course of his study of algebraic roots of polynomials. Thought to be the first to use 'groupe' as a mathematical term. Died from wounds in a duel at 21 after writing up essential parts of his theory the night before.

pxEvaristegalois

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Arthur Cayley  (1821-1895) 

Cayley's Theorem: All finite groups are isomorphic to a subgroup of the symmetry group

Cayley

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Sophus Lie  (1842-1899) 

Lie Groups

pxSophusLie

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Felix Klein  (1845-1925) 

Lie Groups and Geometry

pxFelixKlein

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Hendrik Lorentz  (1853-1928)

HendrikAntoonLorentz

 

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Henri Poincare  (1853-1928)

YoungPoincare

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Elie Cartan  (1869-1951) 

Classification of semisimple Lie groups and algebras, differential geometry and Lie groups

Cartan

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Hermann Weyl  (1885-1955) 

Group theory in quantum mechanics, Weyl-Heisenberg group, symplectic group, topological groups, representation theory

Weyl

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Eugene Wigner  (1902-1995) 

Group theory in quantum mechanics, Special relativity in terms of the unitary representations of the Poincare group

Wigner4

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George Mackey  (1902-1995) 

Unitary representations of groups including semidirect product groups

GWMackeyc1980s

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